


The Integers

by rathrunpredictabl



Series: Miscellenous Shatterdome Moments [3]
Category: Pacific Rim (2013)
Genre: Gen, maths tutoring
Language: English
Status: Completed
Published: 2013-11-25
Updated: 2013-11-25
Packaged: 2018-01-02 01:41:15
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 868
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/1051053
Author URL: https://archiveofourown.org/users/rathrunpredictabl/pseuds/rathrunpredictabl
Summary: <blockquote class="userstuff">
              <p>Occasionally, Mako likes to wander through the archive of files on her personal tablet. The contents of "2018-19 Maths tutoring\Exercises\Favorites" always make her smile. </p>
<p>(I wholeheartedly accept the headcanon that Mako received eclectic and biased tutoring from the Kai-Sci duo.)</p>
            </blockquote>





	The Integers

A blackboard with area x-squared is cleaned every four days with a mixture of 2 parts fluid A to 3 parts fluid B. Incredibly, this amount is exactly enough to clean the board.

Write an equation to describe the consumption of fluids A and B over 30 days.

* * *

A scientist has twelve samples of kaiju tissue. The samples are 14cm by 8cm by 3cm. Of these, three were badly preserved, and will rot at a rate of 2 cubic centimetres per day for the first 4 days, and 5 cubic centimetres per 12 hours for the next 7 days. The other nine are suspended in out-of-date biogel and will decay at a rate of 1 cubic centimetre per 12 hours.

After five days, how much kaiju tissue remains for the scientist to study? (answer in cubic centimetres)

At what point in time will there be exactly half the tissue remaining?

The scientist studies the samples one by one, spending three hours on each sample, without proper isolation techniques. If the samples emit a noxious gas at a rate of 6 cubic millilitres per sample per 5 hours, and assuming a working day of 14 hours, how long will it take to poison the scientist's lab partner? Take into account the degradation of the samples.

* * *

A Breach alert is sounded at 09:35. If a Jaeger sets off on foot from the dock at 10:07 at a speed of 46mph, and the Kaiju is moving at 67mph, at what time will they clash?

How much ground will the Kaiju have covered before the Jaeger intercepts it?

If the Jaeger is airlifted, its speed increases by 38mph. Recalculate to include an airdrop.

Recalculate to include headwind of 46mph.

The corpse of the Kaiju degrades at a rate of 3 cubic centimetres per five minutes. It takes a science team 1 hour 6 minutes to arrive on the scene. Assuming that the Jaeger did not remove any of its limbs or appendages, what percentage of the carcass will remain by the time the team arrives?

It takes 15 minutes to safely collect one sample of tissue. If the xenobiologist heading the team directs them to ignore safety protocol and act faster, thereby shaving 0.7 hours off the collection time, how many samples will they be able to preserve?

* * *

A zen garden with length 5m, width 3m and depth 0.2m is filled with sand.

What is the volume of the empty garden?

A bag contains 1.5 cubic metres of sand and costs 4 HKD. How many bags of sand will it take to completely re-fill the garden? How much will this cost?

Four spheres are placed in the gravel, with diameters 30cm, 89cm, 53cm and 50cm. Assuming the spheres are exactly half-buried in the sand, what is the total volume of sand in the garden?

What is the surface area of the garden available to be raked?

A girl rakes sand very carefully at a rate of 16cm per second. How long will it take her to rake the whole garden? Assume she rakes the whole area vertically first, then returns to make circles around the spheres. (Yes, I am aware this is not how a garden is raked; you may calculate with genuine technique if you wish.)

* * *

It takes 4 carrots, 2 onions, 6 potatoes and 4 leeks to make 2l of good soup, and 3 carrots, 1 onion, 4 potatoes and 2 leeks to make 1.5l of average soup.

How much soup can be made with 60 carrots, 80 onions, 180 potatoes and 70 leeks?

What should be the proportion of good to average soup to make best use of the resources?

* * *

If the temperature is -9C at midnight, and falls by 1 degree every hour until dawn, at what point will it be too cold to move? Calculate for the rest of the week with reference to sunrise and sunset.

* * *

It takes four hours to compile fifteen hours worth of programming in one language, and seven hours to compile nineteen hours worth of programming in another. One algorithm takes ten minutes to code. The first programme contains six hundred and seventeen algorithms; the second contains seven hundred and two.

What is the rate of compilation for the two languages?

What is the fastest amount of time in which the programmer can complete his work?

Recalculate, but this time remove the hours you factored in for sleeping and eating.

* * *

If a scientist steals food from the fridge on average four times per week, and if one box in ten is poisoned, how long will it take for the scientist to realise his mistake?

* * *

Chuck runs at a speed of 15kph, and Mako runs at a speed of 14kph. One circuit of the Shatterdome is 6km.

How long will it take each of them to complete one circuit?

How much faster does the loser have to run in order to win?

Mako takes a shortcut through LOCCENT maintenance that removes 23m from the distance. Chuck realises this at 4.6km round, and speeds up to 17kph.

How long before he overtakes Mako?

How much faster does Mako have to run in order to win the race?

**Author's Note:**

> Title is two words of the Leopold Kronecker quote I am 100% convinced gave Hermann his last name: "Die ganzen Zahlen har der liebe Gott gemacht, alles andere ist Menschenwerk." _God made the integers, all else is the work of man._
> 
> I have the abstract mathematical sense of a polychaete worm, so these problems are probably painfully inaccurate and/or impossible to solve, for which I apologise, but the idea of Hermann snarking about life on the 'domes via Mako's homework appeals to me, and I suppose is my small contribution to the fanon.


End file.
